The gunman killed 18-year-old Reese Fallon of Toronto and a 10-year-old girl who has not been publicly identified.
Hussain’s mental health problems – he suffered depression and psychosis according to his family – have raised questions about how he got a gun.
It was still not known how Hussain managed to obtain the firearm.
A candlelight vigil is planned Wednesday night for the victims of Sunday’s mass shooting on in Toronto’s Greektown.
Despite the family’s statement, the media has sought to whip up fears revolving around gang violence and terrorism with Toronto’s chief of police stating, “It’s way too early to rule out anything”.
The Canadian police identified him as 29-year-old Faisal Hussain.
Police executed a search warrant on Monday at an apartment in the Thorncliffe Park Drive area as part of their investigation.
Canada overhauled its gun-control laws after the country’s worst mass shooting in 1989, when gunman Marc Lepine killed 14 women and himself at Montreal’s Ecole Polytechnique college.
Councillors approved a motion to urge the federal government to forbid the sale of handguns in the city and for the province to outlaw the sale of handgun ammunition in Toronto.
In a speech to council just hours after the shooting, Mayor John Tory said there is a growing problem of people improperly acquiring guns that were originally purchased legally. Gun violence is nearly unheard of in the area and in Toronto, and the realization that a neighbour had gotten a handgun was deeply unsettling to many of Hussain’s neighbours.
Police though say they have nothing to suggest that that is in anyway true at the moment though and that they are continuing to investigate for a motive.
The 13 people wounded range from ages 17 to 59, police said.
Hussain is a Muslim, and DawaNet, a Toronto Muslim charitable association, and Islamic Relief Canada have teamed up with dozens of other Muslim organizations to decry the shootings and fundraise for the victims.
A video taken by a witness showed a man dressed all in black walking quickly down a sidewalk and firing three shots into at least one shop or restaurant in Greektown, a residential area of million-dollar homes that is crowded with restaurants and cafes.
CBS News reported on Tuesday that, according to a law enforcement source, Hussain had visited ISIS websites and “may have expressed support for the terrorist group”.
“I’ll be going to mr greek tonight to have a gyro.opa!” someone named RearViewMirror replied, just one of many responses to Spencer-Nairn’s suggestion.
Nearly three days after two people were shot and killed in Toronto, and after local authorities said their killings had nothing to do with terrorism, ISIS has claimed credit for the attack.